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Li Zhang, Gen Qi Xu, Nikos E Mastorakis, A new approach for stabilization of Heat-ODE cascaded systems with boundary delayed control, IMA Journal of Mathematical Control and Information, Volume 39, Issue 1, March 2022, Pages 112–131, https://doi.org/10.1093/imamci/dnab037
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Abstract
The uniform stabilization problem is addressed for a Heat-ODE cascaded system with boundary delayed control. A simple, direct and easily calculated controller is proposed, in which the known control law is sufficiently applied. With the controller the cascaded system with delayed control is exponentially stabilized. In particular, in the proof of stability, a resolvent for a more complicated integral equation is given. As an application, an equivalent transformation between the closed loop system and a stable system is constructed. The effectiveness of the control-predictor is shown by simulation in the presence of control delay.